Page 232 - Soil and water contamination, 2nd edition

Substance transport 219

Figure 11.14 Contact angle between a liquid and a solid or another immiscible liquid. If the contact angle is
> 110°, the liquid has a low wettability (left); if the contact angle is < 70°, the liquid has a high wettability (right).
produce a contact angle of more than 110° and are thus non-wetting relative to water. This
brings about that in a soil or sediment that contains both water and a NAPL, water spreads
preferentially across solid surfaces and occupies the smaller pore spaces, while the NAPLs
are restricted to the larger pores. A few rules of the thumb to determine whether a fluid is
wetting or non-wetting are given in Table 11.3
The interference of the fluids during flow results in a reduction of the hydraulic
conductivity K (see Box 11.III). In general, the hydraulic conductivity is dependent on both
s
the properties of the fluid (water) and the properties of the media (aquifer materials):
k g
K s (11.44)
M
2
-1
where K = the saturated hydraulic conductivity [L T ], k = the intrinsic permeability [L ],

s
-3
-2
ρ = fluid density [M L ], g = gravitational acceleration constant [L T ], and μ = dynamic
-1
-1
viscosity [M L T ]. The properties of the medium are embedded in the intrinsic
permeability k, and the properties of the fluid are contained in the density and viscosity
parameters. The flow rate of a fluid depends not only on the hydraulic conductivity,
but also – according to Darcy’s law (see Box 11.III, Equation 11.IIIh) – on the gradient in
hydraulic head . The hydraulic head consists of three components: the pressure head, the
elevation head, and the velocity head. Because flow velocity in groundwater is slow, the
velocity head is ignored, so the hydraulic head can be expressed as:
P
h z (11.45)
g
-1
-2
where h = hydraulic head [L], P = pressure [M L T ], and z = the elevation [L]. Combining
Equation (11.43), Equation (11.44), and Darcy’s law (Equation 11.IIIh) for one-dimensional
flow of fluid i in a homogeneous medium gives:
k
q i g z P (11.46)
i i i
M
i
-1
where q = the flow of the ith fluid per unit area [L T ], k = the effective permeability
i i
-1
-1
2
of the medium to the ith fluid [L ], μ = dynamic viscosity of the ith fluid [M L T ],
i
Table 11.3 Wetting and non-wetting fluids in different mixtures of air, water, and NAPLs .
Mixture Wetting fluid Non-wetting fluid
Air–water water air
Air–NAPL NAPL air
Water–NAPL water NAPL

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